Secondary Spectrum Auctions for Symmetric and Submodular Bidders

Abstract: We study truthful auctions for secondary spectrum usage in wireless networks. In this scenario, n communication requests need to be allocated to k available channels that are subject to interference and noise. We present the first truthful mechanisms for secondary spectrum auctions with symmetric or submodular valuations. Our approach to model interference uses an edge-weighted conflict graph, and our algorithms provide asymptotically almost optimal approximation bounds for conflict graphs with a small inductive independence number rho << n. This approach covers a large variety of interference models such as, e.g., the protocol model or the recently popular physical model of interference. For unweighted conflict graphs and symmetric valuations we use LP-rounding to obtain $O(\rho)$-approximate mechanisms; for weighted conflict graphs we get a factor of O(rho (log n + log k)). For submodular users we combine the convex rounding framework of Dughmi et al [STOC 2011] with randomized meta-rounding to obtain O(rho)-approximate mechanisms for matroid-rank-sum valuations; for weighted conflict graphs we can fully drop the dependence on k to get O(rho log n). We conclude with promising initialresults for deterministically truthful mechanisms that allow approximation factors based on rho.